Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
8166 conjugacy classes of subgroups.
The subgroup lattice has 571 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3459 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #39384 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #39383 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #37770 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #37768 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #36117 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #36101 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #35001 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #34984 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | C2×#2361 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C4×#543 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#550 | C22 | 1 | 2 | yes | complemented |
| 13 | #3459 | — | 2 | 32 | no | — |
| 14 | C2×#543 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#539 | C22 | 1 | 12 | yes | complemented |
| 16 | C2×#538 | C22 | 1 | 12 | yes | complemented |
| 17 | C2×#534 | C22 | 1 | 6 | yes | — |
| 18 | C2×#534 | C22 | 1 | 6 | yes | — |
| 19 | C2×#529 | C22 | 1 | 12 | yes | complemented |
| 20 | C2×#525 | C22 | 1 | 12 | yes | complemented |
| 21 | C22×#121 | C22 | 1 | 3 | yes | — |
| 22 | C22×C4×D4 | C22 | 1 | 6 | yes | — |
| 23 | C22×C4×D4 | C22 | 1 | 3 | yes | complemented |
| 24 | C23×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 25 | #2856 | C22 | 1 | 6 | yes | — |
| 26 | #2856 | C22 | 1 | 6 | yes | — |
| 27 | #2854 | C22 | 1 | 12 | yes | complemented |
| 28 | #2847 | C22 | 1 | 12 | yes | complemented |
| 29 | #2733 | C22 | 1 | 12 | yes | complemented |
| 30 | #2732 | C22 | 1 | 12 | yes | complemented |
| 31 | #2727 | C22 | 1 | 12 | yes | complemented |
| 32 | #2714 | C22 | 1 | 24 | yes | complemented |
| 33 | #2694 | C22 | 1 | 24 | yes | complemented |
| 34 | #2682 | C22 | 1 | 12 | yes | complemented |
| 35 | #2656 | C22 | 1 | 6 | yes | — |
| 36 | #2656 | C22 | 1 | 6 | yes | — |
| 37 | #2618 | C22 | 1 | 12 | yes | complemented |
| 38 | #2617 | C22 | 1 | 12 | yes | complemented |
| 39 | #2552 | C22 | 1 | 6 | yes | complemented |
| 40 | #2548 | C22 | 1 | 6 | yes | complemented |
| 41 | #2541 | C22 | 1 | 6 | yes | complemented |
| 42 | #2539 | C22 | 1 | 24 | yes | complemented |
| 43 | #2538 | C22 | 1 | 6 | yes | complemented |
| 44 | #2512 | C22 | 1 | 12 | yes | complemented |
| 45 | #2501 | C22 | 1 | 12 | yes | complemented |
| 46 | #2479 | C22 | 1 | 24 | yes | complemented |
| 47 | #2456 | C22 | 1 | 24 | yes | complemented |
| 48 | #2454 | C22 | 1 | 12 | yes | complemented |
| 49 | #2448 | C22 | 1 | 12 | yes | complemented |
| 50 | #2445 | C22 | 1 | 12 | yes | complemented |
| 51 | #2433 | C22 | 1 | 12 | yes | complemented |
| 52 | #2425 | C22 | 1 | 24 | yes | complemented |
| 53 | #2425 | C22 | 1 | 24 | yes | complemented |
| 54 | #2424 | C22 | 1 | 24 | yes | complemented |
| 55 | #2424 | C22 | 1 | 24 | yes | complemented |
| 56 | #2414 | C22 | 1 | 12 | yes | complemented |
| 57 | #2407 | C22 | 1 | 12 | yes | complemented |
| 58 | #2366 | C22 | 1 | 6 | yes | complemented |
| 59 | #2361 | C22 | 1 | 12 | yes | complemented |
| 60 | #2361 | C22 | 1 | 24 | yes | complemented |
| 61 | #2361 | C22 | 1 | 12 | yes | complemented |
| 62 | #2354 | C22 | 1 | 6 | yes | complemented |
| 63 | Q8×C4⋊C4 | C22 | 1 | 2 | yes | complemented |
| 64 | #2329 | C22 | 1 | 6 | yes | complemented |
| 65 | #2329 | C22 | 1 | 6 | yes | complemented |
| 66 | #2315 | C22 | 1 | 3 | yes | — |
| 67 | C4×C22⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 68 | C4×C22⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 69 | C2×#390 | C22 | 1 | 3 | yes | complemented |
| 70 | C2×#389 | C22 | 1 | 3 | yes | complemented |
| 71 | C2×#388 | C22 | 1 | 6 | yes | complemented |
| 72 | C2×#386 | C22 | 1 | 6 | yes | — |
| 73 | C2×#385 | C22 | 1 | 6 | yes | complemented |
| 74 | C2×C4×C4⋊C4 | C22 | 1 | 3 | yes | complemented |
| 75 | C2×C4×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 76 | C22×#41 | C23 | 1 | 4 | yes | — |
| 77 | C23×D4 | C23 | 1 | 6 | yes | — |
| 78 | C23×D4 | C23 | 1 | 3 | yes | — |
| 79 | C24×C4 | C23 | 1 | 6 | yes | — |
| 80 | C24×C4 | C23 | 1 | 2 | yes | — |
| 81 | C24×C4 | C23 | 1 | 1 | yes | characteristic |
| 82 | #550 | — | 4 | 8 | no | — |
| 83 | #543 | D4 | 1 | 16 | yes | complemented |
| 84 | #539 | — | 2 | 96 | no | — |
| 85 | #538 | — | 2 | 96 | no | — |
| 86 | #534 | — | 2 | 48 | no | — |
| 87 | #534 | — | 4 | 24 | no | — |
| 88 | C2×#127 | C23 | 1 | 6 | yes | — |
| 89 | C2×#127 | C23 | 1 | 6 | yes | — |
| 90 | #529 | — | 2 | 96 | no | — |
| 91 | C2×#126 | C23 | 1 | 24 | yes | — |
| 92 | C2×#125 | C23 | 1 | 12 | yes | — |
| 93 | C2×#124 | C23 | 1 | 12 | yes | — |
| 94 | #525 | — | 2 | 96 | no | — |
| 95 | C2×#123 | C23 | 1 | 24 | yes | — |
| 96 | C2×#123 | C23 | 1 | 24 | yes | — |
| 97 | C2×#123 | C23 | 1 | 24 | yes | — |
| 98 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 99 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 100 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 101 | C2×#121 | — | 2 | 24 | no | — |
| 102 | C2×#121 | C23 | 1 | 12 | yes | — |
| 103 | C2×#121 | C23 | 1 | 12 | yes | — |
| 104 | C2×#121 | C23 | 1 | 12 | yes | — |
| 105 | C2×#121 | C23 | 1 | 12 | yes | — |
| 106 | C2×#121 | C23 | 1 | 12 | yes | — |
| 107 | C2×#121 | C23 | 1 | 12 | yes | — |
| 108 | C2×#121 | C23 | 1 | 12 | yes | — |
| 109 | C2×#121 | C23 | 1 | 12 | yes | — |
| 110 | C2×#121 | C23 | 1 | 12 | yes | — |
| 111 | C2×#120 | C23 | 1 | 24 | yes | — |
| 112 | C2×#120 | C23 | 1 | 24 | yes | — |
| 113 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 114 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 115 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 116 | C2×C4×D4 | — | 2 | 48 | no | — |
| 117 | C2×C4×D4 | — | 4 | 12 | no | — |
| 118 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 119 | C2×C4×D4 | C23 | 1 | 24 | yes | — |
| 120 | C2×C4×D4 | C23 | 1 | 24 | yes | — |
| 121 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 122 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 123 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 124 | C2×#117 | C23 | 1 | 12 | yes | — |
| 125 | C22×C4⋊C4 | — | 4 | 4 | no | — |
| 126 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 127 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 128 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 129 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 130 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 131 | C22×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 132 | C22×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 133 | C22×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 134 | C22×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 135 | C22×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 136 | C22×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 137 | C22×C42 | C23 | 1 | 6 | yes | — |
| 138 | C22×C42 | C23 | 1 | 3 | yes | — |
| 139 | C22×C42 | C23 | 1 | 3 | yes | — |
| 140 | #399 | C23 | 1 | 24 | yes | — |
| 141 | #399 | C23 | 1 | 24 | yes | — |
| 142 | #398 | C23 | 1 | 24 | yes | — |
| 143 | #397 | C23 | 1 | 24 | yes | — |
| 144 | #396 | C23 | 1 | 24 | yes | — |
| 145 | #396 | C23 | 1 | 24 | yes | — |
| 146 | #394 | C23 | 1 | 24 | yes | — |
| 147 | #394 | C23 | 1 | 24 | yes | — |
| 148 | #394 | C23 | 1 | 24 | yes | — |
| 149 | #392 | C23 | 1 | 24 | yes | — |
| 150 | #392 | C23 | 1 | 24 | yes | — |
| 151 | #392 | C23 | 1 | 24 | yes | — |
| 152 | #391 | C23 | 1 | 6 | yes | — |
| 153 | #391 | C23 | 1 | 6 | yes | — |
| 154 | #390 | C23 | 1 | 12 | yes | — |
| 155 | #390 | C23 | 1 | 12 | yes | — |
| 156 | #390 | C23 | 1 | 12 | yes | — |
| 157 | #390 | C23 | 1 | 12 | yes | — |
| 158 | #390 | C23 | 1 | 12 | yes | — |
| 159 | #390 | C23 | 1 | 12 | yes | — |
| 160 | #390 | C23 | 1 | 12 | yes | — |
| 161 | #390 | C23 | 1 | 12 | yes | — |
| 162 | #390 | C23 | 1 | 12 | yes | — |
| 163 | #390 | C23 | 1 | 12 | yes | — |
| 164 | #389 | C23 | 1 | 6 | yes | — |
| 165 | #389 | C23 | 1 | 6 | yes | — |
| 166 | #389 | C23 | 1 | 12 | yes | — |
| 167 | #389 | C23 | 1 | 12 | yes | — |
| 168 | #389 | C23 | 1 | 12 | yes | — |
| 169 | #389 | C23 | 1 | 12 | yes | — |
| 170 | #388 | C23 | 1 | 24 | yes | — |
| 171 | #388 | C23 | 1 | 24 | yes | — |
| 172 | #388 | C23 | 1 | 24 | yes | — |
| 173 | #388 | C23 | 1 | 24 | yes | — |
| 174 | #387 | C23 | 1 | 12 | yes | — |
| 175 | #387 | C23 | 1 | 12 | yes | — |
| 176 | #386 | C23 | 1 | 24 | yes | — |
| 177 | #386 | C23 | 1 | 24 | yes | — |
| 178 | #386 | C23 | 1 | 24 | yes | — |
| 179 | #386 | C23 | 1 | 24 | yes | — |
| 180 | #385 | C23 | 1 | 12 | yes | — |
| 181 | #385 | C23 | 1 | 12 | yes | — |
| 182 | #385 | C23 | 1 | 24 | yes | — |
| 183 | #385 | C23 | 1 | 24 | yes | — |
| 184 | #384 | C23 | 1 | 6 | yes | — |
| 185 | #384 | C23 | 1 | 6 | yes | — |
| 186 | #380 | C23 | 1 | 6 | yes | — |
| 187 | #380 | C23 | 1 | 6 | yes | — |
| 188 | #380 | C23 | 1 | 12 | yes | — |
| 189 | #380 | C23 | 1 | 12 | yes | — |
| 190 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 191 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 192 | C4×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 193 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 194 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 195 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 196 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 197 | C2×#95 | C23 | 1 | 3 | yes | — |
| 198 | C2×#95 | C23 | 1 | 3 | yes | — |
| 199 | C2×#95 | C23 | 1 | 6 | yes | — |
| 200 | C2×#95 | C23 | 1 | 6 | yes | — |
| 201 | C25 | C24 | 1 | 6 | yes | — |
| 202 | C25 | C24 | 1 | 1 | yes | characteristic |
| 203 | C2×#41 | — | 2 | 16 | no | — |
| 204 | C2×#41 | — | 4 | 8 | no | — |
| 205 | C2×#41 | — | 8 | 4 | no | — |
| 206 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 207 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 208 | C22×D4 | — | 2 | 24 | no | — |
| 209 | C22×D4 | — | 2 | 24 | no | — |
| 210 | C22×D4 | — | 2 | 24 | no | — |
| 211 | C22×D4 | — | 2 | 12 | no | — |
| 212 | C22×D4 | — | 4 | 6 | no | — |
| 213 | C22×D4 | — | 4 | 6 | no | — |
| 214 | C22×D4 | C24 | 1 | 24 | yes | — |
| 215 | C22×D4 | C24 | 1 | 6 | yes | — |
| 216 | C22×D4 | C24 | 1 | 6 | yes | — |
| 217 | C22×D4 | C24 | 1 | 12 | yes | — |
| 218 | C22×D4 | C24 | 1 | 12 | yes | — |
| 219 | C22×D4 | C24 | 1 | 12 | yes | — |
| 220 | C22×D4 | C24 | 1 | 12 | yes | — |
| 221 | C23×C4 | — | 2 | 8 | no | — |
| 222 | C23×C4 | — | 2 | 24 | no | — |
| 223 | C23×C4 | — | 4 | 2 | no | — |
| 224 | C23×C4 | — | 4 | 2 | no | — |
| 225 | C23×C4 | — | 4 | 4 | no | — |
| 226 | C23×C4 | — | 4 | 12 | no | — |
| 227 | C23×C4 | — | 8 | 2 | no | — |
| 228 | C23×C4 | — | 8 | 6 | no | — |
| 229 | C23×C4 | #41 | 1 | 8 | yes | complemented |
| 230 | C23×C4 | C24 | 1 | 6 | yes | — |
| 231 | C23×C4 | C24 | 1 | 6 | yes | — |
| 232 | C23×C4 | C24 | 1 | 12 | yes | — |
| 233 | C23×C4 | C24 | 1 | 3 | yes | — |
| 234 | C23×C4 | C24 | 1 | 3 | yes | — |
| 235 | C23×C4 | C24 | 1 | 3 | yes | — |
| 236 | C23×C4 | C24 | 1 | 6 | yes | — |
| 237 | C23×C4 | C24 | 1 | 12 | yes | — |
| 238 | C23×C4 | C24 | 1 | 3 | yes | — |
| 239 | C23×C4 | C24 | 1 | 3 | yes | — |
| 240 | C23×C4 | C24 | 1 | 3 | yes | — |
| 241 | #127 | — | 4 | 12 | no | — |
| 242 | #127 | — | 4 | 12 | no | — |
| 243 | #126 | — | 2 | 96 | no | — |
| 244 | #125 | — | 2 | 48 | no | — |
| 245 | #124 | — | 2 | 48 | no | — |
| 246 | #123 | — | 2 | 96 | no | — |
| 247 | #123 | — | 2 | 96 | no | — |
| 248 | #123 | — | 4 | 48 | no | — |
| 249 | C22⋊Q8 | — | 2 | 48 | no | — |
| 250 | C22⋊Q8 | C2×D4 | 1 | 48 | yes | complemented |
| 251 | C22⋊Q8 | C2×D4 | 1 | 48 | yes | complemented |
| 252 | #121 | — | 2 | 48 | no | — |
| 253 | #121 | — | 2 | 48 | no | — |
| 254 | #121 | — | 2 | 48 | no | — |
| 255 | #121 | — | 2 | 48 | no | — |
| 256 | #121 | — | 2 | 48 | no | — |
| 257 | #121 | — | 4 | 24 | no | — |
| 258 | #121 | — | 4 | 24 | no | — |
| 259 | #121 | — | 4 | 24 | no | — |
| 260 | #121 | — | 8 | 12 | no | — |
| 261 | #120 | — | 2 | 96 | no | — |
| 262 | #120 | — | 4 | 48 | no | — |
| 263 | C4×Q8 | — | 2 | 16 | no | — |
| 264 | C4×Q8 | — | 4 | 4 | no | — |
| 265 | C4×Q8 | — | 4 | 4 | no | — |
| 266 | C4×D4 | — | 2 | 48 | no | — |
| 267 | C4×D4 | — | 2 | 24 | no | — |
| 268 | C4×D4 | — | 2 | 96 | no | — |
| 269 | C4×D4 | — | 2 | 96 | no | — |
| 270 | C4×D4 | — | 4 | 12 | no | — |
| 271 | C4×D4 | — | 4 | 24 | no | — |
| 272 | #117 | — | 2 | 48 | no | — |
| 273 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 274 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 275 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 276 | C2×C4⋊C4 | — | 4 | 6 | no | — |
| 277 | C2×C4⋊C4 | — | 4 | 12 | no | — |
| 278 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 279 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 280 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 281 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 282 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 283 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 284 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 285 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 286 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 287 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 288 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 289 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 290 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 291 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 292 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 293 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 294 | C2×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 295 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 296 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 297 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 298 | C2×C22⋊C4 | — | 4 | 12 | no | — |
| 299 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 300 | C2×C22⋊C4 | C2×D4 | 1 | 24 | yes | — |
| 301 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 302 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 303 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 304 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 305 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 306 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 307 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 308 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 309 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 310 | C2×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 311 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 312 | C2×C42 | — | 2 | 24 | no | — |
| 313 | C2×C42 | — | 4 | 6 | no | — |
| 314 | C2×C42 | — | 4 | 6 | no | — |
| 315 | C2×C42 | C24 | 1 | 12 | yes | — |
| 316 | C2×C42 | C24 | 1 | 6 | yes | — |
| 317 | C2×C42 | C24 | 1 | 12 | yes | — |
| 318 | C2×C42 | C24 | 1 | 6 | yes | — |
| 319 | C2×C42 | C24 | 1 | 6 | yes | — |
| 320 | C2×C42 | C24 | 1 | 6 | yes | — |
| 321 | #95 | C24 | 1 | 12 | yes | — |
| 322 | #95 | C24 | 1 | 12 | yes | — |
| 323 | #95 | C24 | 1 | 12 | yes | — |
| 324 | #95 | C24 | 1 | 12 | yes | — |
| 325 | #95 | C24 | 1 | 24 | yes | — |
| 326 | #95 | C24 | 1 | 12 | yes | — |
| 327 | #95 | C24 | 1 | 12 | yes | — |
| 328 | C24 | — | 2 | 12 | no | — |
| 329 | C24 | — | 2 | 12 | no | — |
| 330 | C24 | — | 2 | 12 | no | — |
| 331 | C24 | — | 4 | 1 | no | — |
| 332 | C24 | — | 4 | 1 | no | — |
| 333 | C24 | — | 4 | 1 | no | — |
| 334 | C24 | — | 4 | 1 | no | — |
| 335 | C24 | — | 4 | 6 | no | — |
| 336 | C24 | — | 4 | 6 | no | — |
| 337 | C24 | — | 4 | 6 | no | — |
| 338 | C24 | — | 4 | 6 | no | — |
| 339 | C24 | C22×D4 | 1 | 4 | yes | — |
| 340 | C24 | C2×#41 | 1 | 4 | yes | — |
| 341 | C24 | H(5,𝔽2) | 1 | 4 | yes | — |
| 342 | C24 | C25 | 1 | 12 | yes | — |
| 343 | C24 | C25 | 1 | 3 | yes | — |
| 344 | #41 | — | 8 | 32 | no | — |
| 345 | C2×Q8 | — | 4 | 2 | no | — |
| 346 | C2×Q8 | — | 4 | 2 | no | — |
| 347 | C2×Q8 | — | 4 | 2 | no | — |
| 348 | C2×Q8 | — | 4 | 2 | no | — |
| 349 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 350 | C2×Q8 | C22×D4 | 1 | 8 | yes | — |
| 351 | C2×D4 | — | 2 | 48 | no | — |
| 352 | C2×D4 | — | 2 | 48 | no | — |
| 353 | C2×D4 | — | 2 | 48 | no | — |
| 354 | C2×D4 | — | 2 | 24 | no | — |
| 355 | C2×D4 | — | 2 | 24 | no | — |
| 356 | C2×D4 | — | 2 | 12 | no | — |
| 357 | C2×D4 | — | 2 | 12 | no | — |
| 358 | C2×D4 | — | 2 | 12 | no | — |
| 359 | C2×D4 | — | 2 | 12 | no | — |
| 360 | C2×D4 | — | 4 | 6 | no | — |
| 361 | C2×D4 | — | 4 | 6 | no | — |
| 362 | C2×D4 | — | 4 | 48 | no | — |
| 363 | C2×D4 | — | 4 | 12 | no | — |
| 364 | C2×D4 | — | 4 | 12 | no | — |
| 365 | C2×D4 | — | 4 | 12 | no | — |
| 366 | C2×D4 | — | 4 | 12 | no | — |
| 367 | C2×D4 | — | 4 | 12 | no | — |
| 368 | C2×D4 | — | 4 | 12 | no | — |
| 369 | C2×D4 | — | 4 | 12 | no | — |
| 370 | C2×D4 | — | 4 | 12 | no | — |
| 371 | C2×D4 | — | 4 | 12 | no | — |
| 372 | C2×D4 | — | 4 | 12 | no | — |
| 373 | C2×D4 | — | 4 | 96 | no | — |
| 374 | C22×C4 | — | 2 | 6 | no | — |
| 375 | C22×C4 | — | 2 | 6 | no | — |
| 376 | C22×C4 | — | 2 | 12 | no | — |
| 377 | C22×C4 | — | 2 | 12 | no | — |
| 378 | C22×C4 | — | 2 | 12 | no | — |
| 379 | C22×C4 | — | 2 | 12 | no | — |
| 380 | C22×C4 | — | 2 | 12 | no | — |
| 381 | C22×C4 | — | 2 | 6 | no | — |
| 382 | C22×C4 | — | 2 | 6 | no | — |
| 383 | C22×C4 | — | 2 | 24 | no | — |
| 384 | C22×C4 | — | 2 | 12 | no | — |
| 385 | C22×C4 | — | 2 | 24 | no | — |
| 386 | C22×C4 | — | 2 | 24 | no | — |
| 387 | C22×C4 | — | 4 | 16 | no | — |
| 388 | C22×C4 | — | 4 | 3 | no | — |
| 389 | C22×C4 | — | 4 | 3 | no | — |
| 390 | C22×C4 | — | 4 | 3 | no | — |
| 391 | C22×C4 | — | 4 | 3 | no | — |
| 392 | C22×C4 | — | 4 | 3 | no | — |
| 393 | C22×C4 | — | 4 | 6 | no | — |
| 394 | C22×C4 | — | 4 | 12 | no | — |
| 395 | C22×C4 | — | 4 | 3 | no | — |
| 396 | C22×C4 | — | 4 | 3 | no | — |
| 397 | C22×C4 | — | 4 | 3 | no | — |
| 398 | C22×C4 | — | 4 | 3 | no | — |
| 399 | C22×C4 | — | 4 | 6 | no | — |
| 400 | C22×C4 | — | 4 | 6 | no | — |
| 401 | C22×C4 | — | 4 | 12 | no | — |
| 402 | C22×C4 | — | 4 | 12 | no | — |
| 403 | C22×C4 | — | 4 | 3 | no | — |
| 404 | C22×C4 | — | 8 | 48 | no | — |
| 405 | C22×C4 | — | 8 | 16 | no | — |
| 406 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 407 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 408 | C22×C4 | C2×#41 | 1 | 12 | yes | — |
| 409 | C22×C4 | C2×#41 | 1 | 12 | yes | — |
| 410 | C22×C4 | C25 | 1 | 6 | yes | — |
| 411 | C22×C4 | C25 | 1 | 6 | yes | — |
| 412 | C22×C4 | C25 | 1 | 6 | yes | — |
| 413 | C22×C4 | C25 | 1 | 12 | yes | — |
| 414 | C22×C4 | C25 | 1 | 6 | yes | — |
| 415 | C22×C4 | C25 | 1 | 6 | yes | — |
| 416 | C22×C4 | C25 | 1 | 3 | yes | — |
| 417 | C22×C4 | C25 | 1 | 2 | yes | — |
| 418 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 419 | C4⋊C4 | — | 2 | 48 | no | — |
| 420 | C4⋊C4 | — | 2 | 24 | no | — |
| 421 | C4⋊C4 | — | 2 | 24 | no | — |
| 422 | C4⋊C4 | — | 2 | 12 | no | — |
| 423 | C4⋊C4 | — | 2 | 12 | no | — |
| 424 | C4⋊C4 | — | 2 | 12 | no | — |
| 425 | C4⋊C4 | — | 2 | 6 | no | — |
| 426 | C4⋊C4 | — | 4 | 6 | no | — |
| 427 | C4⋊C4 | — | 4 | 6 | no | — |
| 428 | C4⋊C4 | — | 4 | 6 | no | — |
| 429 | C4⋊C4 | — | 4 | 6 | no | — |
| 430 | C4⋊C4 | — | 4 | 12 | no | — |
| 431 | C4⋊C4 | — | 4 | 12 | no | — |
| 432 | C4⋊C4 | — | 4 | 6 | no | — |
| 433 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 434 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 435 | C4⋊C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 436 | C22⋊C4 | — | 2 | 24 | no | — |
| 437 | C22⋊C4 | — | 2 | 48 | no | — |
| 438 | C22⋊C4 | — | 2 | 48 | no | — |
| 439 | C22⋊C4 | — | 2 | 48 | no | — |
| 440 | C22⋊C4 | — | 2 | 48 | no | — |
| 441 | C22⋊C4 | — | 2 | 24 | no | — |
| 442 | C22⋊C4 | — | 4 | 12 | no | — |
| 443 | C22⋊C4 | — | 4 | 24 | no | — |
| 444 | C22⋊C4 | — | 4 | 24 | no | — |
| 445 | C22⋊C4 | — | 4 | 24 | no | — |
| 446 | C22⋊C4 | C22×D4 | 1 | 48 | yes | — |
| 447 | C42 | — | 2 | 24 | no | — |
| 448 | C42 | — | 2 | 24 | no | — |
| 449 | C42 | — | 2 | 12 | no | — |
| 450 | C42 | — | 2 | 12 | no | — |
| 451 | C42 | — | 4 | 6 | no | — |
| 452 | C42 | — | 4 | 6 | no | — |
| 453 | C23 | — | 2 | 3 | no | — |
| 454 | C23 | — | 2 | 3 | no | — |
| 455 | C23 | — | 2 | 3 | no | — |
| 456 | C23 | — | 2 | 3 | no | — |
| 457 | C23 | — | 2 | 12 | no | — |
| 458 | C23 | — | 2 | 12 | no | — |
| 459 | C23 | — | 2 | 12 | no | — |
| 460 | C23 | — | 2 | 12 | no | — |
| 461 | C23 | — | 2 | 12 | no | — |
| 462 | C23 | — | 2 | 12 | no | — |
| 463 | C23 | — | 2 | 12 | no | — |
| 464 | C23 | — | 4 | 4 | no | — |
| 465 | C23 | — | 4 | 4 | no | — |
| 466 | C23 | — | 4 | 4 | no | — |
| 467 | C23 | — | 4 | 4 | no | — |
| 468 | C23 | — | 4 | 4 | no | — |
| 469 | C23 | — | 4 | 4 | no | — |
| 470 | C23 | — | 4 | 24 | no | — |
| 471 | C23 | — | 4 | 24 | no | — |
| 472 | C23 | — | 4 | 24 | no | — |
| 473 | C23 | — | 8 | 12 | no | — |
| 474 | C23 | — | 8 | 12 | no | — |
| 475 | C23 | — | 8 | 12 | no | — |
| 476 | C23 | — | 8 | 12 | no | — |
| 477 | C23 | #550 | 1 | 16 | yes | complemented |
| 478 | C23 | C23×D4 | 1 | 6 | yes | — |
| 479 | C23 | C22×#41 | 1 | 6 | yes | — |
| 480 | C23 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 481 | C23 | C26 | 1 | 1 | yes | characteristic |
| 482 | Q8 | — | 4 | 8 | no | — |
| 483 | Q8 | — | 4 | 8 | no | — |
| 484 | D4 | — | 4 | 24 | no | — |
| 485 | D4 | — | 4 | 96 | no | — |
| 486 | D4 | — | 4 | 24 | no | — |
| 487 | D4 | — | 8 | 24 | no | — |
| 488 | D4 | — | 8 | 24 | no | — |
| 489 | D4 | — | 16 | 12 | no | — |
| 490 | D4 | — | 16 | 12 | no | — |
| 491 | C2×C4 | — | 2 | 2 | no | — |
| 492 | C2×C4 | — | 2 | 6 | no | — |
| 493 | C2×C4 | — | 2 | 3 | no | — |
| 494 | C2×C4 | — | 2 | 6 | no | — |
| 495 | C2×C4 | — | 2 | 3 | no | — |
| 496 | C2×C4 | — | 2 | 6 | no | — |
| 497 | C2×C4 | — | 2 | 2 | no | — |
| 498 | C2×C4 | — | 2 | 6 | no | — |
| 499 | C2×C4 | — | 2 | 24 | no | — |
| 500 | C2×C4 | — | 2 | 12 | no | — |
| 501 | C2×C4 | — | 2 | 6 | no | — |
| 502 | C2×C4 | — | 2 | 12 | no | — |
| 503 | C2×C4 | — | 2 | 6 | no | — |
| 504 | C2×C4 | — | 2 | 6 | no | — |
| 505 | C2×C4 | — | 2 | 6 | no | — |
| 506 | C2×C4 | — | 2 | 12 | no | — |
| 507 | C2×C4 | — | 2 | 6 | no | — |
| 508 | C2×C4 | — | 2 | 6 | no | — |
| 509 | C2×C4 | — | 2 | 6 | no | — |
| 510 | C2×C4 | — | 2 | 6 | no | — |
| 511 | C2×C4 | — | 2 | 6 | no | — |
| 512 | C2×C4 | — | 4 | 12 | no | — |
| 513 | C2×C4 | — | 4 | 12 | no | — |
| 514 | C2×C4 | — | 4 | 12 | no | — |
| 515 | C2×C4 | — | 4 | 48 | no | — |
| 516 | C2×C4 | — | 4 | 24 | no | — |
| 517 | C2×C4 | — | 4 | 24 | no | — |
| 518 | C2×C4 | — | 8 | 24 | no | — |
| 519 | C2×C4 | — | 8 | 6 | no | — |
| 520 | C2×C4 | — | 8 | 6 | no | — |
| 521 | C2×C4 | — | 8 | 12 | no | — |
| 522 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 523 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 524 | C2×C4 | C22×#41 | 1 | 6 | yes | — |
| 525 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 526 | C2×C4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 527 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 528 | C2×C4 | #585 | 1 | 2 | yes | — |
| 529 | C22 | — | 2 | 6 | no | — |
| 530 | C22 | — | 2 | 6 | no | — |
| 531 | C22 | — | 2 | 6 | no | — |
| 532 | C22 | — | 2 | 6 | no | — |
| 533 | C22 | — | 2 | 6 | no | — |
| 534 | C22 | — | 2 | 6 | no | — |
| 535 | C22 | — | 4 | 16 | no | — |
| 536 | C22 | — | 4 | 12 | no | — |
| 537 | C22 | — | 4 | 12 | no | — |
| 538 | C22 | — | 4 | 12 | no | — |
| 539 | C22 | — | 4 | 12 | no | — |
| 540 | C22 | — | 4 | 12 | no | — |
| 541 | C22 | — | 4 | 12 | no | — |
| 542 | C22 | — | 4 | 12 | no | — |
| 543 | C22 | — | 8 | 48 | no | — |
| 544 | C22 | C2×#550 | 1 | 12 | yes | — |
| 545 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 546 | C22 | C23×#41 | 1 | 1 | yes | characteristic |
| 547 | C22 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 548 | C22 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 549 | C22 | C2×#585 | 1 | 1 | yes | characteristic |
| 550 | C22 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 551 | C22 | 2−1+6 | 1 | 1 | yes | characteristic |
| 552 | C4 | — | 2 | 4 | no | — |
| 553 | C4 | — | 2 | 12 | no | — |
| 554 | C4 | — | 2 | 12 | no | — |
| 555 | C4 | — | 2 | 6 | no | — |
| 556 | C4 | — | 4 | 6 | no | — |
| 557 | C4 | — | 4 | 6 | no | — |
| 558 | C4 | — | 4 | 6 | no | — |
| 559 | C4 | — | 4 | 12 | no | — |
| 560 | C4 | #3459 | 1 | 4 | yes | complemented |
| 561 | C2 | — | 2 | 12 | no | — |
| 562 | C2 | — | 8 | 12 | no | — |
| 563 | C2 | C2×#3459 | 1 | 1 | yes | characteristic |
| 564 | C2 | C22×#550 | 1 | 1 | yes | characteristic |
| 565 | C2 | #62845 | 1 | 1 | yes | characteristic |
| 566 | C2 | #62895 | 1 | 1 | yes | characteristic |
| 567 | C2 | #62905 | 1 | 1 | yes | characteristic |
| 568 | C2 | D4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 569 | C2 | #62988 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3459 | C2 | semidirect |
| 2. #39384 | C2 | semidirect |
| 3. #39383 | C2 | semidirect |
| 4. #37770 | C2 | semidirect |
| 5. #37768 | C2 | semidirect |
| 6. #36117 | C2 | semidirect |
| 7. #36101 | C2 | semidirect |
| 8. #35001 | C2 | semidirect |
| 9. #34984 | C2 | semidirect |
| 10. C2×#2361 | C2 | semidirect |
| 11. C4×#543 | C2 | semidirect |
| 12. C2×#550 | C22 | semidirect |
| 15. C2×#539 | C22 | semidirect |
| 16. C2×#538 | C22 | semidirect |
| 19. C2×#529 | C22 | semidirect |
| 20. C2×#525 | C22 | semidirect |
| 23. C22×C4×D4 | C22 | semidirect |
| 27. #2854 | C22 | semidirect |
| 28. #2847 | C22 | semidirect |
| 29. #2733 | C22 | semidirect |
| 30. #2732 | C22 | semidirect |
| 31. #2727 | C22 | semidirect |
| 32. #2714 | C22 | semidirect |
| 33. #2694 | C22 | semidirect |
| 34. #2682 | C22 | semidirect |
| 37. #2618 | C22 | semidirect |
| 38. #2617 | C22 | semidirect |
| 39. #2552 | C22 | semidirect |
| 40. #2548 | C22 | semidirect |
| 41. #2541 | C22 | semidirect |
| 42. #2539 | C22 | semidirect |
| 43. #2538 | C22 | semidirect |
| 44. #2512 | C22 | semidirect |
| 45. #2501 | C22 | semidirect |
| 46. #2479 | C22 | semidirect |
| 47. #2456 | C22 | semidirect |
| 48. #2454 | C22 | semidirect |
| 49. #2448 | C22 | semidirect |
| 50. #2445 | C22 | semidirect |
| 51. #2433 | C22 | semidirect |
| 52. #2425 | C22 | semidirect |
| 53. #2425 | C22 | semidirect |
| 54. #2424 | C22 | semidirect |
| 55. #2424 | C22 | semidirect |
| 56. #2414 | C22 | semidirect |
| 57. #2407 | C22 | semidirect |
| 58. #2366 | C22 | semidirect |
| 59. #2361 | C22 | semidirect |
| 60. #2361 | C22 | semidirect |
| 61. #2361 | C22 | semidirect |
| 62. #2354 | C22 | semidirect |
| 63. Q8×C4⋊C4 | C22 | semidirect |
| 64. #2329 | C22 | semidirect |
| 65. #2329 | C22 | semidirect |
| 67. C4×C22⋊Q8 | C22 | semidirect |
| 68. C4×C22⋊Q8 | C22 | semidirect |
| 69. C2×#390 | C22 | semidirect |
| 70. C2×#389 | C22 | semidirect |
| 71. C2×#388 | C22 | semidirect |
| 73. C2×#385 | C22 | semidirect |
| 74. C2×C4×C4⋊C4 | C22 | semidirect |
| 83. #543 | D4 | semidirect |
| 229. C23×C4 | #41 | semidirect |
| 250. C22⋊Q8 | C2×D4 | semidirect |
| 251. C22⋊Q8 | C2×D4 | semidirect |
| 477. C23 | #550 | semidirect |
| 560. C4 | #3459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3459 | 2 |
| #39384 | 2 |
| #39383 | 2 |
| #37770 | 2 |
| #37768 | 2 |
| #36117 | 2 |
| #36101 | 2 |
| #35001 | 2 |
| #34984 | 2 |
| C2×#2361 | 2 |
| C4×#543 | 2 |